Q. 34.0( 4 Votes )
The base edges of two square pyramids are in the ratio 1 : 2 and their heights in the ratio 1 : 3. The volume of the first is 180 cubic centimeters. What is the volume of the second?
Answer :
Let the volume of first pyramid be V1
Let the base edge of first pyramid be a1
Let the height of first pyramid be h1
Let the volume of second pyramid be V2
Let the area of first pyramid be a2
Let the height of first pyramid be h2
We know that,
Volume of a pyramid 
Volume of a first pyramid
…..(1)
Volume of a second pyramid
…(2)
Given: 
⇒ a2 = 2a1 …(a)
Given: 
⇒ h2 = 3h1 …(b)
Consider, Volume of a second pyramid
(from a and b)
⇒ V2 = 12×V1
⇒ V2 = 12×180 = 2160cm3
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